AstroPhyz

Black Holes

Black holes are arguably the most mysterious and captivating objects in the universe. Personally, I dream of studying them at university. They have been featured in many science fiction books and movies, such as Nolan’s Interstellar. But how do they really look like? What rules govern them and how do they form? I’ll try to answer some of these questions in this post.

What is a black hole?

A black hole is a region of space from which nothing, even light, can escape. This means that we can’t see them directly. We can detect black holes by looking at the stars around them. In April 2019, scientists at ETH did just that and unveiled the first ever image of a black hole. Of course, we already predicted them in the 1960s, as they seemed to naturally follow from general relativity.

Image of the M87 black hole. It lies 55 million light-years away from Earth and has the mass of around 6.5 billion Suns.

Black holes generate tremendous gravitational fields. You may be asking, how can gravity attract light, since photons are massless? Newton’s equation does require mass to be present in order to feel the force of gravity, but general relativity does not. Gravitational deflection of light is something that even our sun does, and it has been experimentally tested many times. These gravitational lenses can allow us to see stars that are behind our sun. I’ll probably make a separate post on this topic in the future.

At the center of a black hole there is a singularity. It is a region of infinite density, where the curvature of spacetime becomes infinite. It has zero volume and it is a place where laws of general relativity break down. Still not a lot is known about this region. We might need a solid theory of quantum gravity in order to understand what really happens.

How do they form?

Black holes form from the gravitational collapse of huge stars. Technically, everything can be a black hole if it is packed tightly enough. The size required for a body to undergo irreversible collapse is called the Schwarzschild radius. It’s the tipping point for black holes.

Diagram and equation for the Schwarzschild radius. G is the gravitational constant and c is the speed of light, so you can see that the radius for everyday objects is tiny.

Most stars that form black holes are at least 5 times the mass of the Sun. When they collapse, some larger ones explode as supernovas. These gorgeous explosions are the reason for the prevalence of some elements in the universe and definitely deserve an article of their own.

Characteristics

There are many ways to characterise black holes. Firstly, black holes nomen omen act as ideal blackbodies. So one of the ways of characterising them is through temperature. Stephen Hawking writes about this extensively in A Brief History of Time.

Black holes are extremely cold on the inside, but very hot just outside the event horizon. This is because the matter falling into the black hole gets accelerated to near the speed of light, so the particles have huge average kinetic energy. You might be thinking that the inside of the black hole should have no temperature at all, since no electromagnetic radiation can escape it. However, there is Hawking radiation to consider, which I’ll talk about in another post. It arises due to quantum effects near the event horizon. Pretty cool how quantum effects can affect huge cosmic bodies.

A model of Hawking radiation. It is caused by the appearance of virtual particles on the event horizon. When one falls into the black hole, and one escapes, then the black hole loses some of its mass.

Another way to characterise them is through radius. We have already seen the equation for the Schwarzschild radius, but let’s try to get a sense of scale. The radius for our Sun is around 3km. This means that the Sun would have to collapse to the size of a small town in order to become a black hole. What’s interesting is that if the Sun became a black hole right now, we wouldn’t feel a big difference gravitationally.

The largest known black hole has a radius of 1300 AU. That is 1300 times the distance from the Earth to the Sun. Scary. But black holes could be more familiar than it appears. A very probable theory is that the gravitational mass in the center of the Milky Way is a supermassive black hole. Those have a radius up to 400 AU. For a human to become a black hole, they would need to shrink to 1.04×10⁻²⁵ m in radius. That is way smaller than the radius of a proton, which is about 10⁻¹⁵ m.

References

Dunbar, B. (2015, May 21). What is a black hole? NASA. https://www.nasa.gov/audience/forstudents/k-4/stories/nasa-knows/what-is-a-black-hole-k4.html.

Fisher, L. (n.d.). Are black holes hot or cold? BBC Science Focus Magazine. https://www.sciencefocus.com/space/are-black-holes-hot-or-cold/#:~:text=Black%20holes%20are%20freezing%20cold,a%20degree%20above%20absolute%20zero.&text=When%20astronomers%20study%20black%20holes,the%20material%20that%20they%20see.

NASA. (2019, April 19). How scientists captured the first image of a black hole – teachable moments. NASA. https://www.jpl.nasa.gov/edu/news/2019/4/19/how-scientists-captured-the-first-image-of-a-black-hole/.

Wall, M. (2019, April). Scientists get more great looks at the 1st black hole ever photographed. Space.com. https://www.space.com/m87-supermassive-black-hole-observing-campaign.

Wikimedia Foundation. (n.d.). Schwarzschild radius. Wikipedia. https://en.wikipedia.org/wiki/Schwarzschild_radius.

Look Up by Sarah Cruddas

Look Up is a history of space exploration in the 20th century with a strong focus on the purpose of going to space. The second part of the book is solely devoted to giving examples of technologies brought upon by space endeavours and the environmental research conducted by satellites. The final section discusses private space exploration and the end of the stagnation in terms of putting humans on other planetary bodies. It features a foreword by Michael Collins, an Apollo 11 astronaut, in which he discusses the curiosity that drives us to explore space.

Sarah Cruddas (1983-) is a journalist, author and TV presenter from the UK. She holds a BSc in Physics with Astrophysics from the University of Leicester. Credit: David Levenson.

Compared to some of the other books I featured on the blog, I found this one quite repetitive. I bought it with a bunch of other books, telling myself “why not?” because I was interested in the reasons we give for going to space. I was questioning if it was morally correct that the US spent so much money on the Apollo program during a tumultuous period of the civil rights movement and the abhorrent treatment of homosexuals. What I got was a very cliche story about space inspiring people and bringing about teflon. Nonetheless, there are a few good moments here and I am looking forward to her new books.

The best chapters are definitely Where Next? and Look Back. She discusses the story of private space exploration and some of the costs. She brings about this interesting perspective of space exploration being popularised if a famous celebrity and that going to space can make us realise how fragile the Earth is. Imagining billionaires suddenly changing their mind about cutting down the Amazon rainforest for profit just because of spending a few minutes in low Earth orbit seems overly optimistic. Nonetheless, it has happened to astronauts on the Apollo missions and on the ISS. The difference is, the astronauts are scientists and pilots, trailblazers in the field. They are not doing this for fun, but because it is their calling and they don’t have a company board breathing down their neck.

The idea of realising how fragile Earth is by going to space is first introduced in the book by Michael Collins. It reminds me of the pale blue dot image taken by the Voyager spacecraft. In that sense, the main message of the book is clear and powerful. We have to look up, to then look down and get a sense of perspective on our civilisation. If Cruddas could have said that in a more condensed format, I definitely would have liked the book more. However, if you want a decent overview of private space exploration, go read the last two or three chapters and you might just learn something.

References

Cruddas, S. (2020). Look Up: Our story with the stars. HQ.

Gates Cambridge. (2020, June 25). Biography | Gates Cambridge. Gates Cambridge -. https://www.gatescambridge.org/biography/8902/

Something Deeply Hidden by Sean Carroll

We all know that quantum physics is wacky. Yet, our equations are able to make extremely precise predictions. The Higgs boson is a perfect example. We should be proud of that. Although, there is one major problem. Do we understand what quantum mechanics are fundamentally? This is the question that Carroll attempts to answer in his book. He argues that this slightly philosophical area of research is drastically under-appreciated and lacks funding. He also argues that we live in many universes at once…

Sean M. Carroll is a theoretical physicist interested in quantum mechanics and cosmology. He is known for dark electromagnetism and f(R) gravity. Some of his other books include *From Eternity to Here*, *The Big Picture* and *The Particle at The End of The Universe*. He is a professor at Caltech.

Let me explain. Our common understanding of quantum mechanics is the Copenhagen interpretation. It was devised mainly by Heisenberg and Born in the 1920s. Its main postulates are that everything is probabilistic and that there is an arbitrary boundary between the ‘classical’ and ‘quantum’ realms. Sean Carroll writes that this is quite a shaky set of ideas. Even Einstein would agree with his famous “God doesn’t play dice”.

The author proposes that the Everettian interpretation of quantum mechanics is the right way to look at the world. The only postulate of this theory is that everything is a smoothly evolving wave function with solutions given by the Schrodinger equation. Particles arise from collapses of the wave function in fields. I won’t get into the details too much because Carroll does a way better job at that.

Hugh Everett III (1930-1982) was a theoretical physicist at Princeton. The many-world theory found very little support across academic institutions in the 50s, so he quit academia for many years. He was just ahead of his time.

You might be wondering: how does this theory interpret uncertainty in measurements? A random electron in space has a 50/50 chance to be either spin-up or spin-down. When the system interacts with an observer, the wave function collapses and we observe either outcome. Here is the cool part. The Everettian interpretation states that when we observe a quantum event, we create two copies of the universe. In one of them the electron is measured to be spin-up, in the other it is spin-down. The world can’t interact with one another, so we never see them manifested in “our” universe. This seems unfalsifiable, but Carroll tries to convince the reader that this is a straightforward prediction arising from a simple postulate. Although, it’s tremendously difficult to grasp it philosophically. This is called the many-worlds interpretation of quantum mechanics.

This book is fantastic. It solely revolves around the argument I just presented, but it goes in depth into other theories such as hidden variables, and gives a great background. The Socratic dialogue between father and daughter is an awesome narrative device for addressing a lot of the concerns with the theory. Although, I have to mention that this shouldn’t be your first book about quantum mechanics. Sometimes Carroll commits huge conceptual leaps, which can be hard to follow. Overall, it’s a phenomenal read on the boundary of philosophy and physics.

The Planet Venus

Venus is the closest planetary neighbour of Earth and the second planet from the Sun. It is named after the Roman goddess of love and beauty, but the conditions and weather are actually quite hellish. Despite being further away from the Sun than Mercury, it is the hottest planet in the Solar System with temperatures reaching 471°C, due to the dense atmosphere that traps heat similar to the greenhouse effect. It also orbits in retrograde. Let’s explore some of the aspects of Earth’s nefarious sister.

A gorgeous image of Venus taken by the Mariner 10 craft in February 1974. Credit: NASA.

Venus has been known to people since ancient times, since it is possible to spot it with a naked eye due to its large apparent brightness. A lot of civilisation thought of it as a star. It took until Copernicus and Galileo came onto the scene, when Venus was finally classified as a planet. Further developments happened in the 18th century. In 1761 Mikhail Lomonosov showed that the planet had a gaseous atmosphere.

To see just how similar Venus is to Earth, let’s look at some numbers. Venus has a radius of 6.051 km, and our home planet has a radius of 6,371 km. Venus has a density of 5.24 g/cm³ and Earth has a density of 5.52 g/cm³. Their masses are also similar, as Venus is around 0.85 times the mass of Earth and their volumes are respectively 928 and 1083 billion km³. Don’t let these size and density similarities fool you, since the climates are vastly different, showing the importance of the distance from a star in planetary systems.

Venus has a very thick atmosphere exerting a pressure 92 times higher than our atmosphere. It is primarly composed of carbon dioxide, with thick clouds of sulfuric acid. This makes it very difficult to observe its surface, but advanced radar systems allow us to take a peak. The surface is similar to other rocky planets, covered with dry oceans, canyons and mountains. Moreover, a significant majority of the plains are covered with volcanic rock, which is evidence for prevalent volcanic activity in the past. Some of these volcanos are theorised to have erupted in the last few hundred years.

You might think that there could not have existed life, due to the harsh climate. Yet, scientists suggest that liquid water could have existed there in the past. Pressure changes the boiling point of water, therefore liquid water could have existed at temperatures as high as 150°C. Later, as the planet warmed up, this water evaporated into the atmosphere. Some experts claim that this is too hot for the existence of life. However, extremophiles are known to live in volcanos and can exist at extreme temperatures. Some can thrive in sulphuric acid pools and some can survive in water of 120°C Therefore, who knows what could have been possible. Maybe some bacteria still live there, but that might be wishful thinking.

Another interesting aspect of Venus is the minute difference in temperature during the day and during the night. There are very high wind speeds in the upper atmosphere that can reach up to 200 mph, which were initially thought to be responsible for a rapid temperature transfer between the side illuminated by sunlight and the dark one. Nonetheless, surface winds were shown to be much less than this value. Another likely explanation is the greenhouse effect that allows the temperature to be retained even if a side is in the dark. Due to its axial tilt, the planet orbits upside down making it not experience significant seasonal changes.

Overall, Venus is a very fascinating planet mainly due to its paradoxical nature. Just like Mars, it is Earth’s neighbour, nonetheless it orbits upside down, in retrograde and is a hellish landscape straight from a science fiction horror.

References

Micropia. (n.d.). Phaser App. https://www.micropia.nl/dossiercontent/microworld/en/12/?ph=1

NASA – The Planet Venus. (2004, April 3). NASA. https://www.nasa.gov/audience/forstudents/5-8/features/F_The_Planet_Venus_5-8.html

National Weather Service. (n.d.). The Planet Venus. https://www.weather.gov/fsd/venus

Venus. (2019, September 26). The Nine Planets. https://nineplanets.org/venus/

Water on Mars

The planet Mars has captured the imagination of science fiction authors and scientists as the best candidate to finding extraterrestrial life in the solar system. The red planet has been featured in numerous movies, most recently in the Martian, as a place to establish a human research base and colony. As far as we know, the main condition for life to occur is water. Mars was likely very similar to Earth, it had a magnetic field and liquid water. Where did this vital resource go? What evidence do we have that there once was water? Let’s examine the mystery of water on Mars.

Dried runoff channels on the surface of Mars serve as some of the best evidence for the presence of water in the past. Based on their age it is estimated that it hasn’t rained on Mars for over 3 billion years. Credit: NASA.

In order to understand the issue of water, we should first talk about the red planet’s atmosphere. When the planet first form, it had a much thicker atmosphere just like Earth. Nevertheless, Mars is much smaller therefore due to the lower gravity, the atmospheric gases floated off into space. This caused the planet to cool and the pressure to fall, which allowed water to sublimate and turn instantly from a solid to a gas (like CO₂ dry ice). This is why we see a dry and cold red planet.

Nowadays the atmosphere has the pressure of 1% of the Earth’s atmospheric pressure at surface level. It is composed primarily of carbon dioxide, nitrogen and argon. There are some water-ice clouds that form around mountain tops, however most clouds are composed of CO₂ .

But wait, you might ask, doesn’t Mars have polar ice caps? Aren’t those made of water? The sublimation of water makes it very difficult to have large liquid beds on the surface, so it accumulates in the colder regions as ice under protective sheets. These are made of dry ice or solid carbon dioxide, and change periodically just like the ice caps of the Earth. In fact, Mars experiences a lot of periodic changes in the weather, similar to the ice-ages of the Earth, suggesting that liquid water exists there in some periods. This is due to the changes in the axis of rotation tilt. Perhaps large comet impacts can also briefly create a thick enough atmosphere for liquid water.

An exaggerated image of the Martian polar ice cap. Credit: NASA.

The best evidence of past water are geological landforms. As seen with the first image, there are dried river channels on the surface of Mars. These were likely caused by permafrost in the soil being rapidly melted during a period of high volcanic activity. Another feature of little gullies and dark streaks on the sides of craters indicates very recent water flow. The gullies do not feature many crater impacts, which means they are young. The water could be coming from underground deposits, heated by the tectonic activity of the interior of Mars. In fact, a large slab of ice was found below the surface in 2015, which could have resulted from snowfall in the past.

The dark streaks visible on the side of a crater. Another possible explanation for them could be landslides. Credit: NASA.

Furthermore, other evidence lies in the large plains in the north, which could have once been an ocean. Mount Sharp was constructed using lake sediments, as the Curiosity rover has shown. Furthermore, wetter soil like clay appears near dry lakes and riverbeds. This suggests, that water was prevalent and existed for long periods of time.

If you want to explore the Martian surface for yourself try Google Mars. I recommend downloading it through Google Earth as it runs smoother. It uses satellite images and surface images from rovers to create a very immersive experience. Try looking for ice on the poles and dried riverbeds.

Many of the aforementioned discoveries happened in the 2010s, which means that with more Mars missions we will discover even more evidence and theories about water on the red planet. Perhaps the manned missions planned by Space X and NASA can accelerate progress and once and for all get down to the bottom of this mystery.

References

Evidence for Water on Mars. (n.d.). Hyperphysics. http://hyperphysics.phy-astr.gsu.edu/hbase/Solar/mars4.html

NASA Confirms Evidence That Liquid Water Flows on Today’s Mars. (2015, September 28). NASA. https://www.nasa.gov/press-release/nasa-confirms-evidence-that-liquid-water-flows-on-today-s-mars/

Tillman, N. T. (2018, August 18). Water on Mars: Exploration & Evidence. Space.Com. https://www.space.com/17048-water-on-mars.html

Water and Life on Mars | Astronomy. (n.d.). Lumen Learning. https://courses.lumenlearning.com/astronomy/chapter/water-and-life-on-mars/

Williams, M. (2015, December 7). Mars compared to Earth. Phys.Org. https://phys.org/news/2015-12-mars-earth.html

Neutron Stars

Neutron stars form from supernova explosions, when the remaining core does not collapse into a black hole. They have a diameter of around 20km, which is the size of a city, but they also contain the equivalent of 1.4 mass of the Sun, making them extremely dense. You probably have heard the famous anecdote that a teaspoon of a neutron star weighs a few tonnes. The supernova explosion also gives them tremendous angular momentum, making them spin up to 43000 times per minute as with PSR J1311-3430.

An artist’s rendition of a neutron star, with the magnetic field lines portrayed. Credit: Casey Reed.

As the name suggests, they are made mostly of neutrons. However, they also made of protons and neutrons, and their structure is very complex. For instance, the surface of a neutron star is composed of a lattice of regular atomic nuclei with electrons flowing between them. It is suggested that they are mostly iron, since it is the most stable nucleus with the highest binding energy per nucleon.

The possible structure and types of matter in a neutron star. Credit: Fridolin Weber.

Neutron stars also exhibit some of the strongest magnetic fields of the universe, trillions of gauss stronger than the magnetic field of Earth, which protects us from the Sun’s powerful radiation. The stars with the strongest magnetic fields are known as magnetars, which have relatively short lifespans and rotate slowly every few seconds. The disturbances in the magnetic field known as Starquakes, result in very powerful gamma ray bursts. One of these bursts in 1979 helped detect magnetars, when two Soviet probes and Helios 2 were hit by a burst of energy for a few milliseconds. A bigger burst could prove deadly to life on Earth, again showing how fragile the existence of our species is.

Some of these highly magnetised stars can also emit X-Ray bursts, and they are known as pulsars. They are the sources of very powerful cosmic rays, which could have been the cause of a cosmic bit flip during the 2003 Belgian election, which is an absolutely crazy story. They are of particular interest to astronomers, as they allowed for the detection of the first exoplanets and they can be used as clocks more accurate than atomic clocks. Some scientists claim they can be used for interstellar navigation, although the massive bursts of radiation would easily destroy a ship from a few parsecs away.

Different types of neutron stars. Credit: NASA.

Furthermore, stars rarely exist by themselves. Binary star systems can often emerge, where you have two stars orbiting a common center of mass. This creates a lot of interesting possibilities for calculation and applications of chaos theory. Take a look at this interesting video by Fabio Pacucci on the three body problem, where three objects exert gravitational forces on each other. For high school students wanting a challenge, take a look at problem 20 from the 2017 Oxford Physics Aptitude Test. Interesting things arise when these binary stars collide in a collision known as a kilonova. In 2017, a merger allowed for another detection of gravitational waves. Some scientist claim that these star mergers are the origin of some heavy elements, such as gold.

My personal favourite pulsar is The Black Widow Pulsar (PSR B1957+20). I just think it has an awesome name and also orbits a brown dwarf, which I think is unique. The upper limit for its estimated mass is 2.4 times the Sun’s mass, which makes it the heaviest neutron star. This puts it close to the Tolman–Oppenheimer–Volkoff limit, which states that a neutron star with a mass greater than 3 times the mass of the Sun, would become a black hole. It is fascinating that a star, an object we can imagine fairly well can become a black hole, something that bends the laws of physics just by adding a little bit more mass.

References

Bit Flip | Radiolab. (2019, May 8). WNYC Studios. https://www.wnycstudios.org/podcasts/radiolab/articles/bit-flip

Bruce Ameismeier Chicago, Illinois. (2017, December 4). Astronomy.Com. https://astronomy.com/magazine/ask-astro/2017/12/stellar-magnets

How small are neutron stars? (2020, March 16). Astronomy.Com. https://astronomy.com/news/2020/03/how-big-are-neutron-stars

Tillman, N. T. (2018, February 24). Neutron Stars: Definition & Facts. Space.Com. https://www.space.com/22180-neutron-stars.html

Wall, M. (2012, October 25). Super-Dense Neutron Star Is Fastest Ever Seen. Space.Com. https://www.space.com/18218-fastest-orbiting-pulsar-neutron-star.html

What are neutron stars made out of? | NewCompStar. (n.d.). NewCompStar. https://compstar.uni-frankfurt.de/outreach/short-articles/what-are-neutron-stars-made-out-of/

Hertzsprung-Russell Diagram

In the previous post, we saw that intensity of radiation emitted by a star is proportional to its temperature to the fourth power. Let’s now use that to find a formula for a star’s luminosity. In order to calculate luminosity, we multiply intensity by the surface area of the object. Since, we assume that all stars are perfect spheres, we can use the formula for sphere surface area.

Around 1900, Ejnar Hertzsprung and Henry Norris Russell independently derived a method for visually classifying stars. They plotted luminosity on the y-axis, and temperature on the x-axis. A very beautiful and clear pattern emerged. It must be noted that often the y-axis represents luminosity divided by the luminosity of our sun. This diagram is particularly useful in showing how a star ages and determining star types.

An HR diagram. The diagonal line from top left to bottom right represents main sequence stars. They are ordinary stars like the sun and every 9 out of 10 are classified in this category.

White dwarfs

White dwarfs are small old stars that were not massive enough to become a neutron star or a black hole. Their cores are made of electron-degenerate matter. Our Sun will become a white dwarf in about 10 billion years. These stars are very dense: they can have a mass of the Sun but the volume of the Earth. They are very hot, but have a low luminosity due to their small radius. Once formed, they continue to cool for a tremendously long time. Perhaps, until the heat death of the universe. They are in the bottom left corner of the HR diagram.

Red giants

Red giants have low temperatures, as seen on the x-axis (be careful as it goes from high to low). Their huge luminosities are due to their enormous radii. They are a step in the life cycle of stars, when a star has ran out of hydrogen in its core. They begin fusing hydrogen from the shell surrounding the core. The Sun will become a red giant in about 5 billion years, eating Mercury Venus and destroying Earth’s habitable zone. They are in the top right corner of the HR diagram.

The size of the Sun as a red giant in 5 billion years. Notice that the outer boundary of the Sun sits very close to Earth’s orbit.

Blue giants

These form analogously to red giants. When the hydrogen fuel in the core is exhausted, the star begins to expand. However, more massive stars become blue giants for a period of time before turning into red giants. Despite their huge temperatures, these stars have similar luminosities to red giants. This is because they are only about 5-10 times the radius of the Sun, while red giants can be up to 100 times larger.

Supergiants

These stars have tremendous diameters of over 300 times the size of the Sun. They are also very rare, as they constitute only about 1% of all stars. They have very short lifetimes of approximately a few million years, which is tiny on the cosmic scale. Some well known examples are Betelgeuse and UY Scuti, the largest known star in the universe. They form from huge stars exhausting the fuel in their cores.

Size comparison between the Sun and UY Scuti.

References

Bowen-Jones, M., & Homer, D. (2014). Ib Physics. Oxford University Press.

Cain, F. (2015, December 25). Blue giant star. Universe Today. https://www.universetoday.com/24587/blue-giant-star/.

Hertzsprung-Russell diagram: Cosmos. Hertzsprung-Russell Diagram | COSMOS. (n.d.). https://astronomy.swin.edu.au/cosmos/h/hertzsprung-russell+diagram.

Redd, N. T. (2018, July 26). What is the Biggest Star? Space.com. https://www.space.com/41290-biggest-star.html.

Redd, N. T. (2018, March 28). Red giant stars: Facts, definition & the future of the sun. Space.com. https://www.space.com/22471-red-giant-stars.html#:~:text=In%20approximately%205%20billion%20years,and%20Venus%2C%20and%20reach%20Earth.

Blackbody Radiation

Blackbody radiation is a fascinating concept that shines some light (hehe) on quantum phenomena and stars. Planck’s research into the ultraviolet catastrophe at the beginning of the 20th century jumpstarted quantum physics.

An ideal blackbody is an object that absorbs all radiation incident on it, and then emits 100% of it. This means that the rate at which it absorbs energy is the same as the rate of energy radiation. What makes blackbodies particularly interesting to study is that the spectrum of the emitted light is dependent only on its temperature.

*Blackbody spectrum. Notice that with increasing temperature, the peak total energy radiated increases, and the peak wavelength decreases (Wien’s law)*.

The Ultraviolet Catastrophe

The way to model the energy of blackbody radiation was using the Rayleigh-Jeans law.

I won’t go too much into the details of its derivation, but the main thing we should take away is that it assumes that the energy of light E(f) is independent of the frequency and that it can take on all values. This law matched experimental predictions for large wavelengths, however, it failed miserably at shorter wavelengths like ultraviolet. The values for energy diverged to infinity!

*Comparison of Rayleigh-Jeans law with Planck’s law. You can see that the Rayleigh law is unbounded for small wavelengths.*

Many physicists tried to solve the ultraviolet catastrophe, but it was Max Planck who finally cracked the mystery. His brilliant insight was that photons were only able to take on discrete (quantized) energy values. The equation for E(f) was hence

The entire equation looks very similar, however, this time it doesn’t diverge. The u(f, T) notation means that this is a function with two variables as its inputs. This is why the temperatures are always labeled or color-coded next to the curves.

The graph we looked at in the beginning is of course the intensity graph, which can be derived from Planck’s law. It is a lot of variables to look at, but the beauty in it all is that thinking about discrete energy levels completely changed physics.

Planck called this a mathematical trick at first since he was unable to explain this quantized nature of light. In 1905, Einstein showed that light also behaves like a particle with quantized energy in his Nobel prize-winning photoelectric effect experiment.

Stefan-Boltzmann law

Blackbody radiation is a very important concept in astrophysics. It can help us understand HR diagrams, habitable zones for exoplanets and the life cycles of stars. Let’s look at the basic equations for stellar radiation and power.

For practical applications, we can assume that object act as ideal blackbodies. This approximation works surprisingly well. Now, when we integrate the spectrum given by Planck’s law, we arrive at a very important result in astrophysics: the Stefan-Boltzmann law.

What this means is that the intensity of radiation is proportional to the fourth power of temperature. This is a key result for HR diagrams and figuring out information about distant stars. I’ll cover HR diagrams in the next post!

A Hertzsprung-Russell diagram from the ESO.

References

Blackbody radiation. Brilliant Math & Science Wiki. (n.d.). https://brilliant.org/wiki/blackbody-radiation/.

Blackbody radiation: Cosmos. Blackbody Radiation | COSMOS. (n.d.). https://astronomy.swin.edu.au/cosmos/b/blackbody+radiation#:~:text=As%20the%20temperature%20of%20the%20blackbody%20increases%2C%20the%20peak%20wavelength,(Stefan%E2%80%93Boltzmann%20Law).

The Editors of Encyclopaedia Britannica. (2019). Stefan-Boltzmann law. Encyclopædia Britannica. https://www.britannica.com/science/Stefan-Boltzmann-law.

The Editors of Encyclopaedia Britannica. (2020). Blackbody. Encyclopædia Britannica. https://www.britannica.com/science/blackbody.

The Jovian Planets

Since I was a kid, the only thing I knew about the four jovian planets was that they are big, gaseous and cold. Yet, they are so much more interesting than it seems at first glance. In this post I’ll talk about some special characteristics of each of them. But why does our solar system have these gaseous planets in the first place?

The solar system formed from a giant interstellar nebula of gas about 4.5 billion of years ago. When the Sun formed during the collapse of the nebula, the clouds of gas began orbiting it. Soon, small planetesimals formed from accreted dust. Terrestrial planets formed in the inner solar systems, since the proximity to the sun allowed only rocks and metals to exist. The lower temperatures in the outer solar system allowed ice and hydrogen compounds to exist. Hydrogen and helium compounds were the primary components of the initial nebula, thus the jovian planets are significantly larger than their terrestrial counterparts.

Jupiter

Jupiter is the biggest and heaviest planet in the solar system. One of its most peculiar features is its heat emission. In fact, due to its internal heat generation it emits almost twice the amount of energy it receives from the Sun. At first glance, it seems that this is due to Jupiter’s large size, since it still retains a lot of heat from accretion and differentiation. However, it is not enough to account for the present rate of heat loss. The leading theory is that Jupiter is still contracting, which converts gravitational potential energy to thermal energy.

Saturn

The most striking features of Saturn are definitely the rings. We think of them as continuous sheets, however they are made out of numerous reflective ice particles. These range from small bits of dust to large boulders. However, I believe that the most interesting thing about the rings are the gaps and ripples.

The gaps happen because gravitational attraction causes particles to bunch up at certain orbital distances and to be pushed away at others. One of the sources of these gravitational tugs are gap moons. They are tiny moons located within the rings. They can create a gap in the rings by keeping a space clear of other particles. They also tug at the edges of the rings, creating beautiful ripples. It might seem that the ripples on each side move in opposite directions. This is because the particles nearer to Saturn orbit faster than the ones further away. This can be explained with Kepler’s second law.

Rings are not unique to Saturn, as all of the other jovian planets also have them. However, they are much darker and and the particles are sparser. Hence, it took a long time to discover them. The rings of Uranus were discovered in 1977, the ones on Jupiter in 1979 by the Voyager, and the ones on Neptune in 1989 by the Voyager 2.

Uranus

Many planets are slightly tilted on their axis. For example, Earth has a 23 degree tilt and Saturn a 27 degree one. However, Uranus is tilted by 98 degrees. It rotates around on its side, which creates the most extreme seasonal variations in the solar system. It is suspected that this tilt is due to a tremendous collision with another body during the planet’s formation.

Due to its crazy tilt, Uranus also rotates in the opposite direction to other planets. Uranus and Venus are the only planets that rotate clockwise around their axis. It is generally accepted that all the planets initially spun counterclockwise, but collisions with Earth sized objects changed the orbits of Uranus and Venus. Collisions with massive bodies were relatively common in the early solar system. The Earth’s moon formed as a result of a collision, which can be seen with the evidence of past volcanic activity on its surface.

Neptune

Neptune is the furthest planet from the Sun. Its gorgeous blue color is given by methane in the atmosphere. Yet, I think its biggest moon, Triton, is the most fascinating aspect of this planet.

Triton is has a surface temperature of −235.2 °C, which makes it even colder than Pluto. It is the only large moon in the solar system that orbits its planet in retrograde. Normally, satellites orbit their host planet in the same direction as the planet’s rotation. However, captured moons like Triton do not always obey this rule.

What’s especially interesting in this case is that Triton seems too large to have been captured. One hypothesis states that Triton was paired with another Kuiper belt object. When they passed close to Neptune, Triton lost energy and got captured, while the other object gained energy and flew away. It’s another example of conversation of energy being used to answer tricky astronomy questions.

Another fascinating thing about this moon is its geological activity. Triton is smaller than our Moon, but the surface contains evident of relatively recent volcanism. Other areas contain “cantaloupe terrain”, which is the result of tectonic activity. Pieces of ice of different densities rose and fell, shaping the terrain. Why would such a cold and small world have tectonic activity? The leading hypothesis is tidal heating, the same thing that drives volcanism on Jupiter’s moon Io. Due to Triton being captured, it can be inferred that it had a very elliptical orbit and quicker rotation. The tidal forces would’ve circularised its orbit and heated the interior, which is why the geological activity rapidly subsided. A fascinating moon in the far reaches of the solar system.

References

A. (2019, August 8). Ring ripples reveal how long a day lasts on Saturn. Science News. https://www.sciencenews.org/article/ring-ripples-reveal-how-long-day-lasts-saturn

Bennett, J. O., Donahue, M., Schneider, N., & Voit, M. (2020). The Cosmic Perspective. Pearson Education, Incorporated.

In Depth | Neptune –. (2020). NASA Solar System Exploration. https://solarsystem.nasa.gov/planets/neptune/in-depth/

In Depth | Triton –. (2020). NASA Solar System Exploration. https://solarsystem.nasa.gov/moons/neptune-moons/triton/in-depth/

Jupiter | Facts, Surface, Moons, Great Red Spot, & Rings. (2020). Encyclopedia Britannica. https://www.britannica.com/place/Jupiter-planet

The Artemis Program

NASA’s website calls the Artemis program Apollo’s twin. Its immediate goal is revitalising the US space program and sending the first woman and person of color to the Moon. It is supposed to be the foundation for a sustained international stay of humanity on the Moon. The end goal is making going to Mars very feasible. NASA also wants to build a base camp on the moon, which would be used to test technologies that later could be sent to Mars. The project was initiated under the Trump administration and accelerated to the deadline of a landing in 2024, (which NASA deems highly unrealistic). This is possibly due to trying to get the US ahead in potential space mining and commercialising of space. Biden’s administration endorsed the program in February. There are many nations involved to help facilitate space mining and an international law that makes it peaceful. Russia has criticised the US for making that law centered around itself.

An artist’s visualisation of the Artemis rocket on the Moon. Credit: NASA.

How does it compare with the Apollo program? I think that the Apollo program was a much greater technological leap than Artemis. Buzz Aldrin questioned the idea to “send a crew to an intermediate point in space, pick up a lander there and go down”. I personally feel that the intermediate step of going to the Moon is unnecessary; I feel like NASA should head straight to Mars like Space X is planning to. The goal of sending more women into space could be also achieved at an even grander scale, if it was on a mission to Mars. I don’t believe that there will be a permanent colony on the Moon simply because it would cost a lot to get astronauts to and from the surface. The ISS is already an immensely expensive project, and astronauts cannot stay on board for more than a few months, due to weightlessness. It might not be as bad on the Moon, but people would not stay there for 20+ years. Furthermore, I think that the ISS achieves the same or even more in terms of benefits to humanity, since it allows for experiments in weightlessness and observation of the Earth. We already know a ton about the Moon, so going back seems pointless when Mars awaits.

Where should we build the Moon research base? I think, the station should be build in one of the flat regions, in order for ease of landing. It should also be on the side that faces the Earth because that might allow for easier communication and psychological comfort for the astronauts.

A detailed plan of the first Artemis mission. Credit; NASA.

Should we bring our own water, or search for it on the Moon? There is Lunar water on the Moon from comets, which was discovered in 1971. Scientists claim that it would make habitation much more feasible, but delivering equipment to extract that water seems more costly than just delivering it. The deposits found so far are relatively small, thus this plan still needs a few more years to work.

I believe that the Artemis program can revitalise the idea of putting people onto other planetary bodies, which can inspire a generation of astronauts and engineers. However, I do not believe that this is a good project for NASA to pursue long term, aside from possible mining. I think it’s time for humanity to take the next big step and go to Mars.

References

Artemis 1. (n.d.). ESA. https://www.esa.int/Science_Exploration/Human_and_Robotic_Exploration/Orion/Artemis_1

Foust, J. (2018, November 16). Advisory group skeptical of NASA lunar exploration plans. SpaceNews. https://spacenews.com/advisory-group-skeptical-of-nasa-lunar-exploration-plans/

Mann, A. (2019, July 3). NASA’s Artemis Program. Space.Com. https://www.space.com/artemis-program.html

NASA ujawnia szczegóły programu Artemis. (2019, May 28). Space24. https://www.space24.pl/nasa-ujawnia-szczegoly-programu-artemis